Definite articles (eg "the") indicate that it is a "known noun phrase" - the noun phrase is known by the listener/reader. Indefinite articles (eg "a") indicate an "unknown noun phrase" - the noun phrase is not one that is directly identifiable by the listener. But there are situations where there is no definite or indefinite article, such as when the possessive form is used. Consider the following sentence:

1. A good idea of Tom's.

We know that #1 is indefinite. But consider the following:

2. Tom's good idea.

Is "good idea" in #2 definite or indefinite? What is the deep structure of #2, above? Is it like "the good idea" (known noun phrase) or like "a good idea" (unknown noun phrase)?

My question: Is "good idea" at number "2" an unknown or a known noun phrase?
– nimaApr 12 '14 at 17:44

1

"Tom's good idea" refers to a known idea. I would say that "Tom's good idea" is equivalent to "the good idea of Tom's" (but "the good idea of Tom's" sounds pretty awkward).
– Tanner SwettApr 12 '14 at 19:44

1

@nima_persian I've tried to clarify the wording in this question. Please, let me know if you feel the new wording has changed the meaning of your original question.
– NicoApr 12 '14 at 20:11

1

Genitive NPs in determiner position are always definite, so if you have to pick one or the other for the phrase's "deep structure", pick the.
– snailplane♦Apr 12 '14 at 21:13

2 Answers
2

This is out of context, so it’s hard to say. I would venture that ‘Tom’s’ in ‘Tom’s good idea’ serves to define the idea, so in a sense it’s functioning like a definite article. It’s not just any good idea, but Tom’s.

You might have a text that starts as follows:

At the meeting, we heard about a good idea for solving the cash flow problem from Tom. Tom’s good idea involved increasing sales through strategic price reduction. [...]

The first mention of the idea uses the indefinite article, but subsequently it’s referred to as Tom’s. You might also have ‘the idea’, ‘this idea’ in place of ‘Tom’s good idea’. In fact, it sounds somewhat unnatural to repeat the adjective, so ‘Tom’s idea’ would actually be better. Hope that helps.

There are several theories of determiners, and it is an area of linguistic study. There are also many variations and special cases, so there's no single rule that covers all situations. One aspect is based on familiarity of the NP to both the speaker and the listener. A related aspect is whether the information is new/unknown/not-yet-introduced or old/known/introduced previously.

In the Noun Phrase (NP) "A good idea of Tom's", the "good idea" is one (indefinite) "idea" of possibly many. For example,

A good idea of Tom's is to build a bridge. The idea is known by the speaker, but the speaker assumes the listener does not know which one he is referring to until after he explains it.

Sometimes the indefinite article is used to introduce an NP and the definite article is used after that. This can be based on the new/old unknown/known aspect of determiner theory:

A good idea of Tom's is to build a bridge. The idea is that if we build a bridge, we can eliminate the ferry and traffic congestion. In the first sentence, the idea is introduced. In the second sentence it should be clear to the listener (reader) to understand which idea is being referred to.

The dog is first being qualified as the one and single "good dog" that is owned by John. As such, this determiner is "definite". In context, the word "good" might also be acting as a determiner. The speaker could be indicating Tom's one particular good dog rather any of his other bad dogs. Otherwise, "good" is simply being descriptive of his dog.

The following is similarly possessive (and determinate):

Tom's good idea

Here the speaker is referring to a particular good idea that Tom has. It is similar to this:

The good idea of Tom's

Finally, note that your phrase "A good idea of Tom's" could be rephrased as "One of Tom's good ideas"

Note that in google search, "unknown noun phrase" does not have many results, so that's not a common terminology in English.